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Chapter 8: Q24 (page 372)

Critical Values. In Exercises 21–24, refer to the information in the given exercise and do the following.

a. Find the critical value(s).

b. Using a significance level of = 0.05, should we reject H0or should we fail to reject H0?

Exercise 20

Short Answer

Expert verified

a. The critical values are -1.96 and 1.96.

b. The decision of the statistical test is to fail to reject the null hypothesis.

Step by step solution

01

Given information

A test statistic value of z=-1.94 is obtained, and the claim to be tested is p=38.

02

Hypotheses and tail of the test

The hypotheses are as follows:

Null Hypothesis: p=38

Alternative Hypothesis: p≠38

Since there is a not equal to sign in the alternative hypothesis, the test is two-tailed.

03

Critical value

a.

Referring to the standard normal table, the critical values of z corresponding to the two-tailed test at α=0.05are -1.96 and 1.96.

04

Decision about the test

b.

If the absolute value of the test statistic is greater than the critical value, then the null hypothesis is rejected; otherwise, not.

Since the absolute value of the test statistic is less than the critical value, the decision is to fail to reject the null hypothesis.

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Most popular questions from this chapter

Final Conclusions. In Exercises 25–28, use a significance level of = 0.05 and use the given information for the following:

a. State a conclusion about the null hypothesis. (Reject H0or fail to reject H0.)

b. Without using technical terms or symbols, state a final conclusion that addresses the original claim.

Original claim: More than 58% of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of 0.3257.

Testing Claims About Proportions. In Exercises 9–32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.

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Testing Claims About Proportions. In Exercises 9–32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.

Testing Effectiveness of Nicotine Patches In one study of smokers who tried to quit smoking with nicotine patch therapy, 39 were smoking one year after the treatment and 32 were not smoking one year after the treatment (based on data from “High-Dose Nicotine Patch Therapy,” by Dale et al., Journal of the American Medical Association, Vol. 274, No. 17). Use a 0.05 significance level to test the claim that among smokers who try to quit with nicotine patch therapy, the majority are smoking one year after the treatment. Do these results suggest that the nicotine patch therapy is not effective?

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